Odds and Expected Returns

By Alex Smith, Last updated Feb 27, 2024

One of the things you need to remember when you’re playing at online casinos is that casinos are businesses; they’re there to make money, and the way they make most of their money is through the casino games on their site.

All casino games (with a few VERY rare exceptions) have their own odds and expected returns – and on this page we’re going to be having a look at what this means for you, the player, when it comes to actually playing these games. Let’s kick things off with a look at slot machines – perhaps the most common type of casino game offered at online casinos today.

Odds and Expected Returns on Slot Machines

The term “expected return” refers to a percentage that mathematically forecasts how much of each slot machine play you will get in return. This means that when you’re playing games with an expected return of 96%, you should expect to receive 96 cents back for every $1 you wager.

This also implies that you will lose 4 percent of each wager you place. The “house edge” is the gap between the projected return and 100 percent of the investment.

In fact, calculating this figure is less difficult than you may imagine. When playing an online slot game, you calculate the likelihood of receiving a particular outcome by the amount of money that is paid out for that particular result. That is the amount of money you will receive from that combination.

When you add all of the returns together, you will get the overall return for the game played.

If you’re talking about any gambling game, this is especially beneficial when you’re talking about slot machine games.

The expected return on a slot machine game varies substantially from one casino to another, and even more often from one machine to another. Even machines that are totally similar to one another may have drastically different odds of producing certain symbols and combos depending on how they are programmed.

However, a slot machine game’s predicted return of 96 percent is not out of the ordinary for this type of game. In fact, 96 percent is a respectable score.

Let’s say you have $600 to spend at the casino, and you decide to play the slot machine that has a 96 percent return on investment. (Of course, the majority of the time, you have no idea what the return on a slot machine game is. Unless an online gambling regulator specifically requires it, most online casinos won’t voluntarily tell you the expected returns of a specific game.

Does this indicate that you’ll be able to walk away from the casino that night with 96 percent of the money you put on the table in question? No, it is not as easy as that.

Most of the time, you’re not going to stick with your original $600 bankroll. Most of the time, you’ll keep putting money into the machine and spinning the reels over and over again. When you place bets on the same amount of money over and over again, you are engaging in what is known as “the grind.”

The 4 percent house edge does not just apply to your total bankroll; it also applies to your individual bets. The 4 percent commission is applied to each and every bet you make on the slot machine.

Consider the following scenario: you’re playing the dollar machines and you’re betting three credits every spin. Every time you spin the wheel, you are putting $3 into action. Let’s also assume you’re spinning the reels at a pace of 500 spins per hour, which is not an unusual rate of play for a slots player.

A Word From Bryan, CEO of Casinomeister

“Now this is where it gets tricky! Obviously to a large extent, what you expect back from a game will depend largely on your strategy. And of course there are games where you cannot generally affect the outcome so much – slots and keno being prime examples. It is worth noting however that online casinos generally (and this is a generalization) offer a better return on games of chance than their Bricks & Mortar counterparts. In the UK for example, “fruit machines” are typically set at between 70% and 80% payouts, whereas the majority of online casinos will typically have expected returns of 90% to 95% on slots. 

The main difference is that online slots tend to offer higher “top payouts” and therefore you are likely to hit longer losing streaks before you hit the big payouts. These big payouts often make up a fair chunk of the expected return, so without them you may find the slots seem meaner than their hardware counterparts.

Before I get into where to play for the best percentages, a final word on slots. You may find that the casinos publish payout percentages for certain groups of games, as determined by independently audited statistics.

That’s about the closest you are going to get to knowing exactly how much online casino slots pay out. However, Wagerworks software also publishes the expected returns on their slots in the “pay tables”. Log into the game, view the paytable and go to the last page and you’ll find the info. 

In general, their slots are set to about 95%-96%, and I’d say this was a fairly accurate indicator for online casinos in general. Much better than land casino slots in general, but it’s still a muddy area, with many operators not publishing exact figures at game level – yet anyway.

However there are some games, like Video Poker, where you can calculate the expected returns and there are several sites out there that will provide you with this information. A great example is Michael Shackleford, highly respected math-head . Michael has a reputation for integrity and mathematical prowess and he also acts as an independent auditor to OddsOn (Vegas Technology) casino software licensee. 

Typically, online casino video poker games will pay out between 97% and 99.5% when played to the correct strategy. Check Michael’s site for expected payouts. And even a small deviation from strategy can make a big difference, so it pays to know your game. Or alternatively, play at a Microgaming “Viper” casino where the software’s “expert mode” holds the cards for you and plays to the optimum strategy!”

The Expected Return of Table Games

As you can probably imagine, like the stock market, different casino games (investments) have different expected return percentages – and this means that you’ll find that casino table games like Blackjack and Baccarat have different expected returns than other casino table games like Craps and 3-Card Poker. Below, we look at a few examples of this

Roulette

Roulette is one of the most popular casino table games in the world and it’s played religiously at both online casinos and land-based casinos. At the Roulette table you’ll find a number of different bet options available to you – and this can make it a little more complex when it comes to multiplying potential outcomes and looking at the expected return. To start off, we’ll begin by looking at the single number bet – a bet where you place a casino chip on a specific number.

With 36 numbers of the Roulette wheel plus zero, there’s a total of 37 different potential outcomes for this bet; however, while the odds of your bet winning is 1/37, the land-based casinos and online casinos only actually pay you out at 35/1. This means that when you’re playing European Roulette the expected return of a single number bet is 2.7%. However, if you choose to play French or American Roulette (different versions of the popular casino table game) then the expected return can be even worse, at 5.3%.

When it comes to other types of bets, things get a little more complicated; let’s look at even money bets. This includes bets like red/black and odd/even; it’s also a 50/50 chance that you’ll win this bet, but because the Roulette wheel contains a zero, it’s not quite this figure; for example, if because the payout is only 1/1, this means the casino’s house edge is thanks to the zero. The odds of winning an even-money bet are 16/37, and the odds of losing are 17/37 – and this means that the expected return of each game played on one of these bet types is also 2.7%. Please note that this is different to the house edge – something that we’re not going to be covering in this article but a topic that’s worth familiarizing yourself with if you get the chance.

Blackjack

Blackjack is another hugely-popular casino game that you’ll find available at virtually every land-based casino and online casino, and it’s popularity can be attributed to a number of reasons; first of all it’s incredibly easy-to-play; you don’t need to understand any complex math to play (unless you’re trying to count cards), it’s a sociable game as you’re not playing against other players and can thus interact with them – and there’s a feeling of comadre when playing in land-based casinos as you’re all trying to beat the dealer at the same time.

However, Blackjack is also hugely popular thanks to the fact that it has a really low house edge – and this means that the expected return is very high; in fact, the chances of you winning an individual Blackjack hand is just under 50% – when playing according to basic strategy – and this can, in some cases, even end up being weighted in favor of the player if card counting techniques are used.

However, it’s impossible to give a specific percentage when it comes to the expected return of a Blackjack game and that’s down to the fact that every land-based casino and online casino tends to use slightly different rules in their Blackjack games. For example, some online casinos will have dealers hit on soft 17s while others will have dealer’s stick; these little nuances within the game can greatly impact the way in which the game plays out – but generally speaking your expected return while playing Blackjack is really quite high!

Craps

Craps is a slightly harder game to calculate the expected return on, and that’s due to the fact that there’s so many different betting options at the table – and there’s also a huge number of different in-game options; for example, the gameplay changes depending on which numbers are rolled. However, as a general rule of thumb when it comes to Craps there’s 11 different outcomes – and these can equate from totals between 2 and 12. However, it’s possible to approach these outcomes in 36 different ways – and the probabilities and odds of each of these needs to be calculated individually.

We’re not going to get into all of the specifics right here, but generally speaking the common bets are fairly easy to work out. For example, if you place a bet on any Craps bets – 2, 3 or 12 – then the payout is calculated as 7.5/1. The house edge of this bet is 5.56%. On the other end of the scale, betting on any seven – generally considered to be the worst bet at the Craps table – has a payout of 4/1, although the house edge is as high as 16.67%.

FAQs

What does RTP mean?

The Return to Player percentage (RTP) is the payout percentage that varies from online Slot game to online Slot game, and from developer to developer. You will be looking for an online Slot machine that has a minimum of 95%, preferably more than that. But let’s say that an online Slot has a 95% RTP.

That means that (over time) out of 100 coins (100%), 95 (95%) go back to the real cash online Slot player. The rest of that percentage is obviously the online casino’s margin. Some online Slot machines will not even reach 91%, and unless for some reason you feel extremely drawn towards this particular online Slot game, you really shouldn’t stick with low payout games like that.

How can I find out the expected return of a casino game?

There’s a couple of ways that you can find out the expected return calculations for casino games you want to play – and the first way is to load up the game and check out the help files. Often, game developers and software providers will include the information about the expected return here.

However, this isn’t always the case – and if you find that an online casino doesn’t show you this information then you can simply reach out to the customer support team and ask them to provide you with more information.

Can historical data be used to predict the outcome of future games?

No; while you can, by looking at historical data, get somewhat of a weighted average of how much a video slot or casino table games has been sticking to its RTP, variance takes over – and the potential outcomes for casino games are so big that it can take billions of spins – years – for a game to actually reach its expected RTP.

Because of this you should never look at the previous results of games and expect that a certain result is more or less likely to come in; even in a fair coin toss it could be heads 20 times in a row – and this is a good example of why there’s never a safe bet at the online casinos when you’re playing games of chance.

Do online casinos have to tell you what the expected return is for their casino games?

Whether or not a casino has to provide you with information about the expected value – and how you can go about calculating expected return – depends largely on the jurisdiction in which the online casino is based. For example, some of the world’s stricter online gambling regulators like the UK Gambling Commission and the MGA does require operators to provide you with information about the expected return of casino games – while other online gambling regulators like Curacao, don’t.

Does the expected return increase the more you bet?

Whether or not the expected return – and your expected return calculations – increases when you increase the size of your stake depends on which type of casino game you’re playing. For most casino table games, the expected return doesn’t increase when you’re playing at higher stakes – even if historical data may imply otherwise.

However, there are certain video slots and classic slot machines – and video pokies – that do increase the RTP if you increase the size of your stake. Generally speaking, when you’re playing some of these classic slot machines you’ll find something in the rules that states something like ‘play at max coin value for the best RTP’ – and this really, is the only time when you should consider playing at higher stakes simply to try and end up actually winning more from the slot.

What casino games offer the best expected return?

This is quite a tough question to answer, as with most casino table games there’s a wide variety of different bets that you can place when playing all casino games on the market. However, as a very general rule of thumb the best casino games that you can play include Blackjack, Craps and Baccarat. All of these casino games have a very low house edge, and this means that the chances of you winning – especially in the short-term – are far greater than

Does calculating expected return improve my chances of winning?

No; while it can certainly be beneficial to have a good idea about the expected return – and what it means for you in terms of your chances of winning while playing certain casino table games and video slots – simply knowing this information doesn’t actually improve or increase your chances of winning – and if anyone tries to tell you otherwise, be warned that they’re not being truthful with you.

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